A spring shoe usually includes vertically spaced top and bottom plates and springs between them. A person fastens his foot (which may have a shoe thereon) to the top plate and can exercise or have fun by using the spring shoe to jump. If an additional stabilizing device is not provided, the top plate has poor stability, in that it can easily shift laterally (from side to side) or longitudinally (forward and rearwardly) with respect to the bottom plate. Also, the top plate can tilt in roll (one side moves down and the other up). Spring shoes are easier to use if motion of the top plate with respect to the bottom plate is limited to vertical motion to provide the spring-aided jump effect, and to tilting in pitch (where the front tilts up or down) to facilitate control of forward and rearward movement. U.S. Pat. No. 1,613,538 by Schad shows a stabilizing mechanism which includes four 2-bar linkages, with each linkage coupling the top and bottom plates. While such linkages resist sideward shifting of the top plate, they do not resist longitudinal shifting or roll of the top plate. Also, such linkages are relatively expensive and fragile because of the numerous lightweight pivot joints. A rugged stabilizing mechanism for a spring shoe, which resisted substantially all motion of the top plate relative to the bottom plate except vertical motion and pivoting in pitch, and which was of relatively simple and rugged construction, would facilitate the provision of easy-to-use spring shoes.